Multidimensional exact solutions to a quasilinear parabolic equation with anisotropic heat conductivity
- 31 Downloads
We prove invariance of a quasilinear parabolic equation with anisotropic heat conductivity in the three-dimensional coordinate space under some equivalence transformations and present some explicit formulas for these transformations. We consider nontrivial reductions of the equation to similar equations of less spatial dimension. Using these results, we construct new exact multidimensional solutions to the equation which depend on arbitrary harmonic functions.
Keywordsquasilinear parabolic heat equation Liouville equation multidimensional exact solution equivalence transformation anisotropy conjugate harmonic function
Unable to display preview. Download preview PDF.
- 2.Galaktionov V. A., Dorodnitsyn V. A., Elenin G. G., et al., “A quasilinear heat equation with a source: blow-up, localization, symmetry, exact solutions, asymptotics, and structures,” in: Contemporary Problems of Mathematics. Modern Achievements [in Russian] VINITI, Moscow, 1986, 28, pp. 95–205 (Itogi Nauki i Tekhniki).Google Scholar
- 4.Ibragimov N. Kh., Transformation Groups in Mathematical Physics [in Russian], Nauka, Moscow (1983).Google Scholar
- 6.Polyanin A. D. and Zaizev V. F., Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, Boca Raton, FL (2003).Google Scholar